Pascal's calculator

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replicas were built. Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry. The cumulative friction and inertia of all these wheels could "...potentially damage the machine if a carry needed to be propagated through the digits, for example like adding 1 to a number like 9,999". The great innovation in Pascal's calculator was that it was designed so that each input wheel is totally independent from all the others and carries are propagated in sequence. Pascal chose, for his machine, a method of re-zeroing that propagates a carry right through the machine. It is the most demanding operation to execute for a mechanical calculator and proved, before each operation, that the carry mechanism of the Pascaline was fully functional. This could be taken as a testament to the quality of the Pascaline because none of the 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet this feature was fully tested on all the machines, by their resets, all the time.

191: 143: 2347: 259: 2217: 31: 267: 39: 2136: 2170:), which provided the exclusive right to design and manufacture calculating machines in France, allowing the Pascaline to be the first calculator sold by a distributor. Pascal feared that craftsmen would not be able to accurately reproduce his Pascaline, which would result in false copies that would ruin his reputation along with the reputation of his machine. In 1645, in order to control the production of his invention, Pascal wrote to Monseigneur Le Chancelier (the chancellor of France, 2256: 2319: 304:", Pascal noted that a machine with 10,000 wheels would work as well as a machine with two wheels because each wheel is independent of the other. When it is time to propagate a carry, the sautoir, under the sole influence of gravity, is thrown toward the next wheel without any contact between the wheels. During its free fall the sautoir behaves like an acrobat jumping from one trapeze to the next without the trapezes touching each other ("sautoir" comes from the French verb 293: 3802: 2272: 2150:, Pascal hoped to provide a shortcut to hours of number crunching performed by workers in professions such as mathematics, physics, astronomy, etc. But, because of the intricacies of the device, the relationship Pascal had with craftsmen, and the intellectual property laws he influenced, the production of the Pascaline was far more limited than he had envisioned. Only 20 Pascalines were produced over the 10 years following its creation. 2141:“The second cause which I foresee capable of giving you umbrage, are (dear reader) the bad copies of this machine which might be produced by the presumption of the craftsmen: on these occasions, I conjure you to carry carefully the spirit of distinction, to keep you from surprise, to distinguish between leprosy and leprosy, and not to judge of the true originals by the imperfect productions of the ignorance and temerity of the workmen” 324: 3812: 3598: 246:

on it are barely visible. On a decimal machine, the digits 0 through 9 are carved clockwise, with each digit positioned between two spokes so that the operator can directly inscribe its value in the window of complements by positioning his stylus in between them and turning the wheel clockwise all the way to the stop lever. The marks on two adjacent spokes flank the digit 0 inscribed on this wheel.

2232:, one of Pascal's contemporaries also working on creating a calculating machine, likely succeeded because of his ability to manage good relations with his craftsmen. Morland proudly attributed part of his invention to the artisans by name– an odd thing for a nobleman to do for a commoner at the time. Morland was able to recruit the best talent in Europe. His first craftsmen was the famous 231:

the wheel clockwise all the way to the stop lever. The number displayed on the corresponding display register will be increased by 5 and, if a carry transfer takes place, the display register to the left of it will be increased by 1. To add 50, use the tens input wheel (second dial from the right on a decimal machine), to add 500, use the hundreds input wheel, etc...

76:, which adds 1 to 9 on one dial, and carries 1 to the next dial when the first dial changes from 9 to 0. His innovation made each digit independent of the state of the others, enabling multiple carries to rapidly cascade from one digit to another regardless of the machine's capacity. Pascal was also the first to shrink and adapt for his purpose a 202: 2357:

started to work on his own calculator after Pascal's death. He first tried to build a machine that could multiply automatically while sitting on top of the Pascaline calculator, assuming incorrectly that all the dials on Pascal's calculator could be operated at the same time. Even though this could

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In other words, the 9's complement of the difference of two numbers is equal to the sum of the 9's complement of the minuend added to the subtrahend. The same principle is valid and can be used with numbers composed of digits of various bases (base 6, 12, 20), like in the surveying or the accounting

384:

The Pascaline is a direct adding machine (it has no crank), so the value of a number is added to the accumulator as it is being dialed in. By moving a display bar, the operator can see either the number stored in the calculator or the complement of its value. Subtractions are performed like additions

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understanding of the inventing process: ideas precede materialisation, as form precedes matter. This naturally led to an emphasis on theoretical purity and an underappreciation for practical work. As Pascal described artisans: “ work through groping trial and error, that is, without certain measures

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The method of re-zeroing that Pascal chose, which propagates a carry right through the machine, is the most demanding task for a mechanical calculator and proves, before each operation, that the machine is fully functional. This is a testament to the quality of the Pascaline because none of the 18th

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when France was occupied by Germany and therefore the main celebration was held in London, England. Speeches given during the event highlighted Pascal's practical achievements when he was already known in the field of pure mathematics, and his creative imagination, along with how ahead of their time

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Pascal's calculator was the most successful mechanical calculator developed in the 17th century for the addition and subtraction of large numbers. The stepped reckoner had a problem in the carry mechanism after more than two consecutive carries, and the other devices had carry mechanisms (one tooth

245:

Four of the known machines have inner wheels of complements, which were used to enter the first operand in a subtraction. They are mounted at the center of each spoked metal wheel and turn with it. The wheel displayed in the picture above has an inner wheel of complements, but the numbers written

230:

For a 10-digit wheel (N), the fixed outside wheel is numbered from 0 to 9 (N-1). The numbers are inscribed in a decreasing manner clockwise going from the bottom left to the bottom right of the stop lever. To add a 5, one must insert a stylus between the spokes that surround the number 5 and rotate

209:

The calculator had spoked metal wheel dials, with the digit 0 through 9 displayed around the circumference of each wheel. To input a digit, the user placed a stylus in the corresponding space between the spokes and turned the dial until a metal stop at the bottom was reached, similar to the way the

283:

Pascal adapted a pawl and ratchet mechanism to his own turret wheel design; the pawl prevents the wheel from turning counterclockwise during an operator input, but it is also used to precisely position the display wheel and the carry mechanism for the next digit when it is pushed up and lands into

275:

Pascal went through 50 prototypes before settling on his final design; we know that he started with some sort of calculating clock mechanism which apparently "works by springs and which has a very simple design", was used "many times" and remained in "operating order". Nevertheless, "while always

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The German calculating-machine inventor Arthur Burkhardt was asked to attempt to put Leibniz' machine in operating condition. His report was favorable except for the sequence in the carry. and "therefore, especially in the case of multiple carry transfers, the operator had to check the result and

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guild in 1631, half-way through Pascal's efforts to create the calculator. This affected Pascal’s ability to recruit talent as guilds often reduced the exchange of ideas and trade; sometimes, craftsmen would withhold their labour altogether to rebel against the nobles. Thus Pascal was in a market

270:

Pascal's adaptation. The blue gear (input) meshes with the yellow gears (processing), which themselves drive the red gear (output). The intersection of two perpendicular cylinders is one point and therefore, in theory, the blue gear and the yellow gear mesh in one single point. Pascal designed a

249:

On four of the known machines, above each wheel, a small quotient wheel is mounted on the display bar. These quotient wheels, which are set by the operator, have numbers from 1 to 10 inscribed clockwise on their peripheries (even above a non-decimal wheel). Quotient wheels seem to have been used

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These marks are used to set the corresponding cylinder to its maximum number, ready to be re-zeroed. To do so, the operator inserts the stylus in between these two spokes and turns the wheel all the way to the stopping lever. This works because each wheel is directly linked to its corresponding

2224:

Pascal operated his project with this hierarchy in mind: he invented and thought, while the artisans simply executed. He hid the theory from artisans, instead promoting that they should simply remember what to do, not necessarily why they should do it, i.e., until "practice has made the rules of

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built the first replica of Schickard's machine but not without adding wheels and springs to finish the design. This detail is not described in Schickard's two surviving letters and drawings. A problem in the operation of the Schickard machine, based on the surviving notes, was found after the

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had written to his friend Johannes Kepler in 1623 and 1624 which contain the drawings of a previously unknown working calculating clock, predating Pascal's work by twenty years. The 1624 letter stated that the first machine to be built by a professional had been destroyed in a fire during its

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which was meant to perform additions, subtractions and multiplications automatically and division under operator control. Leibniz struggled for forty years to perfect this design and produced two machines, one in 1694 and one in 1706. Only the machine built in 1694 is known to exist; it was

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Each dial is associated with a one-digit display window located directly above it, which displays the value of the accumulator for this position. The complement of this digit, in the base of the wheel (6, 10, 12, 20), is displayed just above this digit. A horizontal bar hides either all the

238:, two adjacent spokes are marked; these marks differ from machine to machine. On the wheel pictured on the right, they are drilled dots, on the surveying machine they are carved; some are just scratches or marks made with a bit of varnish, some were even marked with little pieces of paper. 315:

All the sautoirs are armed by either an operator input or a carry forward. To re-zero a 10,000-wheel machine, if one existed, the operator would have to set every wheel to its maximum and then add a 1 to the "unit" wheel. The carry would turn every input wheel one by one in a very rapid

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its next position. Because of this mechanism, each number displayed is perfectly centered in the display window and each digit is precisely positioned for the next operation. This mechanism would be moved six times if the operator dialed a six on its associated input wheel.

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By 1654 he had sold about twenty machines (only nine of those twenty machines are known to exist today), but the cost and complexity of the Pascaline was a barrier to further sales and production ceased in that year. By that time Pascal had moved on to the study of

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display cylinder (it automatically turns by one during a carry operation). To mark the spokes during manufacturing, one can move the cylinder so that its highest number is displayed and then mark the spoke under the stopping lever and the one to the right of it.

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improving on it" he found reason to try to make the whole system more reliable and robust. Eventually he adopted a component of very large clocks, shrinking and adapting for his purpose the robust gears that can be found in a turret clock mechanism called a

311:

Pascal used gravity to arm the sautoirs. One must turn the wheel five steps from 4 to 9 in order to fully arm a sautoir, but the carry transfer will move the next wheel only one step. Thus, much extra energy is accumulated during the arming of a sautoir.

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theory so common that have finally been reduced into art”. This stemmed from his lack of faith in not only the artisanal work process, but in the artisans themselves: “artisans cannot regulate themselves to produce unified machines autonomously."

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Move the display bar down to uncover the complement part of each result cylinder. From this point on, every number dialed into the machine adds its value to the accumulator and therefore decreases the total displayed in the complement window.

134:, the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. It is not clear whether he ever saw Leibniz's device, but he either re-invented it or utilized Leibniz's invention of the step drum. 2400:

that is often mistaken for a mechanical calculator because it has a carry mechanism in between the numbers. But it is actually an abacus, since it requires the operator to handle the machine differently when a carry transfer takes place.

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positions it above this pin ready to push back on it. The sautoir keeps on moving up and suddenly the second carry pin drops it. The sautoir falls of its own weight. During the second phase, the sautoir and the two wheels are completely

150:

Blaise Pascal began to work on his calculator in 1642, when he was 18 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a

344:. During the first phase, the active wheel touches the one that will receive the carry through the sautoir, but it never moves it or modifies it and therefore the status of the receiving wheel has no impact whatsoever on the active wheel. 2335:

construction and that he was abandoning his project. After careful examination it was found, in contradiction to Franz Hammer's understanding, that Schickard's drawings had been published at least once per century starting from 1718.

1407:. It feels like an addition since the only two differences in between an addition and a subtraction are the position of the display bar (direct versus complement) and the way the first number is entered (direct versus complement). 3106: 2665: 2207:

Pascal’s own conduct led to difficulty in recruiting artisans for his project. This was rooted by his belief that matters of the mind trumped those of the body. Pascal was not alone, as many natural philosophers of his time had a

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and proportions regulated by art, produc nothing corresponding to what they had sought, or, what’s more, they make a little monster appear, that lacks its principal limbs, the others being deformed, lacking any proportion.”

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and non-decimal varieties, both of which can be viewed in museums today. They were designed for use by scientists, accountants and surveyors. The simplest Pascaline had five dials; later variants had up to ten dials.

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of a telephone is used. This displayed the number in the windows at the top of the calculator. Then, one simply redialed the second number to be added, causing the sum of both numbers to appear in the accumulator.

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complement numbers when it is slid to the top, or all the direct numbers when it is slid toward the center of the machine. It thereby displays either the content of the accumulator or the complement of its value.

2174:) in his letter entitled "La Machine d’arithmétique. Lettre dédicatoire à Monseigneur le Chancelier". Pascal requested that no Pascaline be made without his permission. His ingenuity garnered the respect of 2178:

of France who granted his request, but it came at a price; craftsmen were not able to legally experiment with Pascal's design, nor were they able to distribute his machine without his permission/guidance.

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The first phase happens when the display register goes from 4 to 9. The two carry pins (one after the other) lift the sautoir pushing on its protruding part marked (3,4,5). At the same time the kicking

226:

was used. The only two differences between an addition and a subtraction are the position of the display bar (direct versus complement) and the way the first number is entered (direct versus complement).

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The operator enters the second operand: 56,789. If he starts with the rightmost number, the second wheel will go from 4 to 5, during the inscription of the 9, because of a carry transmission....

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Most of the machines that have survived the centuries are of the accounting type. Seven of them are in European museums, one belongs to the IBM corporation and one is in private hands.

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The metric system was adopted in France on December 10, 1799, by which time Pascal's basic design had inspired other craftsmen, although with a similar lack of commercial success.

115:), which provided the exclusive right to design and manufacture calculating machines in France. Nine Pascal calculators presently exist; most are on display in European museums. 2146:

Pascal planned to distribute the Pascaline broadly in order to reduce the workload for people who needed to perform laborious arithmetic. Drawing inspiration from his father, a

473: 2204:, who built upon Pascal's calculator later in the 17th century, had the progress for his machine halted due to his artisan selling the machine's parts for financial solvency. 462: 944: 3084: 375:

positions the entire receiving mechanism in its proper place. During the third phase the sautoir, which no longer touches the active wheel, adds one to the receiving wheel.

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or dial the complement of the minuend directly. The display bar is shifted to show the complement's window so that the operator sees the direct number displayed because

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century criticisms of the machine mentioned a problem with the carry mechanism and yet this feature was fully tested on all the machines, by their resets, all the time.

1313: 1265: 876: 1403: 1223: 757: 222:

Since the gears of the calculator rotated in only one direction, negative numbers could not be directly summed. To subtract one number from another, the method of

2378:, the principle of a two-motion mechanical calculator. He was also the first to have cursors to inscribe the first operand and a movable carriage for results. 1024:

Add 1 to the right-most wheel. Each wheel sends its sautoir to the next one, the zeros appear one after another, like in a domino effect, from right to left.

308:, which means to jump). All the wheels (including gears and sautoir) have therefore the same size and weight independently of the capacity of the machine. 2247:

In the end, Pascal succeeded in cementing his name as the sole creator of the Pascaline. The royal patent states that it was his invention exclusively.

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The second wheel from the right has a wheel with 10 spokes contained in a fixed wheel with 20 segments. This could be attributed to a bad restoration.

69:. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction. 65:

in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in

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The machine has to be re-zeroed before each new operation. To reset his machine, the operator has to set all the wheels to their maximum, using the

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wheel) that were limited in their capacity to carry across multiple digits or had no carry mechanism in between the digits of the accumulator.

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Subtractions are performed with the display bar moved closest to the center of the machine showing the complement value of the accumulator.

2608:, p. 29 (1988). "Toutes les machines arithmétiques inventoriées....sauf la machine tardive du C.N.A.M....ont deux rayons contigus marqués". 2374:

manually correct the possible errors". Leibniz had not succeeded in creating a calculator that worked properly, but he had invented the

2240:

for his contributions in producing coinage for England. Morland's other craftsmen were similarly accomplished: the third, Dutchman John

118:

Many later calculators were either directly inspired by or shaped by the same historical influences that had led to Pascal's invention.

2744: 2518: 1654:. Therefore, the pascaline needed wheels in base 6, 10, 12 and 20. Non-decimal wheels were always located before the decimal part. 1519:

Dial the subtrahend (12,345) on the spoked metal wheels. This is an addition. The result, 41,976, is in the 9's complement window.

2381:

There were five additional attempts at designing "direct entry" calculating machines in the 17th century (including the designs of

1075:

Additions are performed with the display bar moved closest to the edge of the machine, showing the direct value of the accumulator.

3628:"Avis nécessaire à ceux qui auront curiosité de voir ladite Machine et s'en servir" (Pascaline, 1635), online text and analysis on 3661: 103:. Pascal built around twenty more machines during the next decade, many of which improved on his original design. In 1649, King 2259:

Pascaline made for French currency which once belonged to Louis Perrier, Pascal's nephew. The least significant denominations,

2200:

that had a scarcity of skills and willing workers. Importantly, artisans were not free as intellectuals to create the machine:

976:

Set all the wheels to their maximum using the marks on two adjacent spokes. Every single wheel is ready for a carry transfer.

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gear that could easily take the strength of the strongest operator and yet added almost zero friction to the entire mechanism

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the first calculator to have a controlled carry mechanism that allowed for an effective propagation of multiple carries

3623: 3489: 3450: 3405: 3384: 3039: 2196: 2054: 948:. The last step can be repeated as long as the subtrahend is smaller than the minuend displayed in the accumulator. 347:

The second phase starts when the display register goes from 9 to 0. The kicking pawl passes its guiding pin and its

2220:

Letter from the French Royal allowing Pascal exclusive rights to his invention. This was arguably the first patent.

2416:, the first machine strong enough to be used daily in an office environment. The Arithmometer was designed around 88:. This innovation allowed the device to resist the strength of any operator input with very little added friction. 2049:

This is the only known machine that came with a box. This is the smallest machine. Was it meant to be portable?

340:

is pulled up, using a pin on the receiving wheel as guidance, but without effect on this wheel because of the top

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The above is an excerpt from Pascal's letter to the Chancellor of France. When translated to English, it states:

401:. So the 9's complement of 4 is 5 and the 9's complement of 9 is 0. Similarly, the 11's complement of 3 is 8. 3815: 2946: 1888: 634: 3366:

Science and Civilization in China: Volume 4, Physics and Physical Technology, Part 2, Mechanical Engineering

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Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage

280:, itself derived from a water wheel mechanism. This could easily handle the strength of an operator input. 190: 2358:

not be done, it was the first time that a pinwheel was described and used in the drawing of a calculator.

614:{\displaystyle {\begin{aligned}CP(A-B)&=10^{n}-1-(A-B)&=10^{n}-1-A+B\\&=CP(A)+B\end{aligned}}} 3654: 1617: 3608: 2923:

Oeuvres: Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir

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during a division to memorize the number of times the divisor was subtracted at each given index.

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rediscovered at the end of the 19th century, having spent 250 years forgotten in an attic at the

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Besides being the first calculating machine made public during its time, the pascaline is also:

182:

The tercentenary celebration of Pascal's invention of the mechanical calculator occurred during

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Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir

2666:

Avis nécessaire à ceux qui auront curiosité de voir la Machine d'Arithmétique et de s'en servir

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after 1671, after trying to add an automatic multiplication feature to the Pascaline. In 1820,

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Histoire des instruments et machines à calculer, trois siècles de mécanique pensante 1642–1942

142: 2409: 1232: 843: 58: 2580: 3730: 3708: 3558: 3523: 3429:

Annales du Conservatoire national des arts et métier, 2e série, tome 5, Le calcul simplifié

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in 1649 that granted him exclusive rights to make and sell calculating machines in France.

3784: 2007: 8: 3703: 3416: 2346: 2159: 104: 3562: 3527: 2865: 262:

A lantern gear used in turret clocks powered by weights that can weigh hundreds of kilos

258: 3478: 3439: 3007: 2991: 2887: 2237: 2216: 3776: 266: 30: 3768: 3713: 3485: 3462: 3446: 3401: 3380: 3350: 3295: 3249: 3035: 2999: 2983: 2942: 2879: 2458: 2453: 2354: 2331: 2135: 1269:

after adding B. In displaying that data in the complement window, the operator sees

1081:

The following table shows all the steps required to compute 12,345 + 56,789 = 69,134

119: 38: 3760: 3011: 2832: 2171: 1677:. In a surveyor's machine (..10,10,6,12,12), the decimal part counted the number of 96: 3566: 3531: 2975: 2891: 2869: 2438: 2362: 2318: 2147: 1999: 127: 2188: 3698: 3500: 3395: 3374: 3056: 2921: 2327: 1657:

In an accounting machine (..10,10,20,12), the decimal part counted the number of

1410:

The following table shows all the steps required to compute 54,321-12,345=41,976

763:

First the complement of the minuend is entered. The operator can either use the

201: 2100:

This machine was bought as a broken music box in a French antique shop in 1942.

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La Machine d'arithmétique. Lettre dédicatoire à Monseigneur le Chancelier, 1645

2433: 2386: 2233: 2229: 3613: 2979: 2632:, Courrier du centre international Blaise Pascal, Clermont-Ferrand, no 8, 1986 2182: 146:

Four Pascalines and a clone from Lépine on display at the CNAM museum in Paris

3830: 3670: 2987: 2883: 2463: 2417: 2375: 2303: 2255: 317: 123: 62: 2289:

the first calculator to be used in an office (his father's to compute taxes)

2236:, who had already received protection and recognition from French statesman 3096:

Encyclopédie de Diderot & d'Alembert, Tome I, 1ère édition, pp. 680-681

3003: 2443: 2413: 2209: 1579: 834:

Then the second number is dialed in and adds its value to the accumulator.

300:

The sautoir is the centerpiece of the pascaline's carry mechanism. In his "

277: 183: 131: 85: 81: 2964:"Reinventing machines: the transmission history of the Leibniz calculator" 1468:

Enter the 9's complement of the minuend. The operator can either use the

1412: 1083: 969: 292: 2448: 2408:

Calculating machines did not become commercially viable until 1851, when

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After re-zeroing the machine, numbers are dialed in one after the other.

211: 108: 2995: 2963: 2782:"Staatliche Kunstsammlungen Dresden - Mathematisch-Physikalischer Salon" 359:

pushes the pin on the receiving wheel and starts turning it. The upper

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the first calculator commercialized (with around twenty machines built)

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In a decimal machine with n dials the 9's complement of a number A is:

164: 77: 3740: 3619:

More detail on the history of the Pascaline and contemporary replicas.

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Catalogue du musée – Section A Instruments et machines à calculer

3285:(in French). Clermont-Ferrand: La Française d'Edition et d'Imprimerie. 3143:

The calculating Clock of Wilhelm Schickard. Retrieved January 31, 2012

175: 3571: 3546: 3536: 3511: 3432:(in French). Paris: Gauthiers-Villars et files, Imprimeurs-Libraires. 2874: 2849: 2175: 363:

is moved to the next space. The operation stops when the protruding

92: 323: 3547:"Blaise Pascal (1623–1662) Tercentenary of the calculating machine" 2510: 2191:. During his time, craftsmen in Europe increasingly organised into 160: 72:

Pascal's calculator was especially successful in the design of its

2097:

5 x 10 + 6 + 12 + 12

1989:

This machine was assembled in the 18th century with unused parts.

95:, he presented the device to the public in 1645, dedicating it to 2275:

View through the back of the above calculator, showing the wheels

2058: 1571: 3639: 2244:, came a famous Dutch family who pioneered the pendulum clock. 3597: 3340:(in French). Paris: Conservatoire National des Arts et Métiers. 3271: 2620:, p. 29 (1988). "...palmette, petits ronds, griffures, vernis". 2167: 882:

The result (A-B) is displayed in the complement window because

152: 112: 3322:(in French). Presses universitaires de France. pp. 20–28. 2283:

the only operational mechanical calculator in the 17th century

3418:

Mechanical arithmetic, or The history of the counting machine

2338:

Bruno von Freytag Loringhoff, a mathematics professor at the

2192: 1612: 66: 2412:

released, after thirty years of development, his simplified

234:

On all the wheels of all the known machines, except for the

2183:

Social context of intellectual collaboration with craftsmen

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or dial the 9's complement of 54,321 (45,678) directly.

3614:

Detailed animation explaining how the Pascaline works.

320:

fashion and all the display registers would be reset.

3624:

More on the 'operating instructions' for a Pascaline.

1379: 1325: 1277: 1235: 1199: 890: 846: 775: 733: 637: 476: 413: 2807:"IBM Archives: Artifacts list for vol. 3, items M-Z" 2668:

Wikisource: La Machine d’arithmétique, Blaise Pascal

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The machine is at zero, the operator enters 12,345.

385:

using some properties of 9's complement arithmetic.

3502:

Recueil de plusieurs machines de nouvelle invention

3445:. Los Alamitos, California: IEEE Computer Society. 3248:(in French). Clermont-Ferrand: Muséum Henri-Lecoq. 2939:

Labour, Science and Technology in France, 1500-1620

393:The 9's complement of any one-digit decimal number 3477: 3461: 3438: 3272:Ellenberger, Michel; Collin, Marie–Marthe (1993). 3034:. The University of Chicago Press. pp. 5–34. 1397: 1361: 1307: 1259: 1217: 938: 870: 811: 751: 709: 613: 456: 2592:Pascal tercentenary celebration, London, (1942). 2195:, such as the English clockmakers who formed the 2021:Marguerite (1646–1733) was Pascal's goddaughter. 1960:Louis Périer, Pascal's nephew, offered it to the 1841:The decimal part of each machine is highlighted. 960: 3828: 3609:Website explaining the operation of a Pascaline. 2745:"Muséum Henri-Lecoq - Ville de Clermont-Ferrand" 2350:Leibniz' drawing showing 365 multiplied by 124. 1705:. Scientific machines just had decimal wheels. 1469: 764: 3584:(in French) (8). Clermont-Ferrand: 4–25. 1986. 3582:Courrier du Centre International Blaise Pascal 3347:Scripta Mathematica (Septembre 1932-Juin 1933) 3331:(in French). Presses universitaires de France. 3320:Le calcul mécanique. Que sais-je ? n° 367 3313:(in French). Presses universitaires de France. 3311:Le calcul mécanique. Que sais-je ? n° 367 3085:Privilège du Roi, pour la Machine Arithmétique 2968:The British Journal for the History of Science 2941:. Cambridge university press. pp. 29–31. 2330:, announced the discovery of two letters that 467:and therefore the 9's complement of (A-B) is: 327:The three phases of a carry transfer operation 91:Pascal designed the machine in 1642. After 50 3655: 3329:Histoire du calcul. Que sais-je ? n° 198 42:Top view and overview of the entire mechanism 3283:Les machines arithmétiques de Blaise Pascal 3246:Les Machines Arithmétiques de Blaise Pascal 3061:(in French). La Haye. pp. vol 4, pg 7. 2907:Les machines arithmétiques de Blaise Pascal 2700: 2698: 2302:the first calculator to be described in an 3662: 3648: 2715: 2713: 2309:the first calculator sold by a distributor 3570: 3535: 3480:Computers: The Life Story of a Technology 3335: 3244:Vidal, Nathalie; Vogt, Dominique (2011). 3243: 2904: 2873: 1866: Machine Name 963:, and then add 1 to the rightmost wheel. 720:This principle applied to the Pascaline: 331:The carry transmission has three phases: 194:Detail of the carry mechanism and of the 3109:La Machine d’arithmétique, Blaise Pascal 3087:La Machine d’arithmétique, Blaise Pascal 2695: 2552: 2550: 2542:La Machine d’arithmétique, Blaise Pascal 2396:Around 1660 Claude Perrault designed an 2361:He then devised a competing design, the 2345: 2317: 2270: 2254: 2215: 2153: 2134: 2131:Limits to distribution and controversies 954: 322: 291: 265: 257: 200: 189: 187:both the machine and its inventor were. 141: 37: 29: 3505:. Paris, France: Jean Batiste Coignard. 3188: 3186: 2847: 2710: 2421: 2326:In 1957, Franz Hammer, a biographer of 2187:Pascal lived in France during France's 710:{\displaystyle CP(A-B-C-D)=CP(A)+B+C+D} 223: 14: 3829: 3274:La machine à calculer de Blaise Pascal 3262: 3054: 2936: 2919: 2830: 3643: 3545:Prof. S. Chapman (October 31, 1942). 3308: 3077: 3029: 3025: 3023: 3021: 2961: 2826: 2824: 2822: 2820: 2547: 2295:the first calculator to be patented ( 3811: 3183: 3099: 2509: 2313: 73: 34:A Pascaline signed by Pascal in 1652 3468:. New York: Reynal & Hitchcock. 3393: 24: 3397:The Universal History of Computing 3267:(in French). La Haye: Chez Detune. 3018: 2930: 2817: 2491: 2026:Musée Henri Lecoq 287: 253: 25: 3858: 3669: 3590: 3512:"Pascal tercentenary celebration" 3372: 2809:. 23 January 2003. Archived from 2055:Mathematisch-Physikalischer Salon 388: 3810: 3801: 3800: 3596: 3421:. Chicago: Washington Institute. 3376:The Universal History of Numbers 2306:(Diderot & d'Alembert, 1751) 457:{\displaystyle CP(A)=10^{n}-1-A} 3441:History of Computing Technology 3221: 3209: 3197: 3171: 3159: 3147: 3136: 3124: 3112: 3090: 3065: 3048: 2955: 2913: 2898: 2841: 2799: 2774: 2762: 2737: 2725: 2683: 2671: 2659: 2647: 2635: 2623: 2611: 2250: 2083:Léon Parcé collection 939:{\displaystyle CP(CP(A-B))=A-B} 3400:. John Wiley & Sons, Inc. 3379:. John Wiley & Sons, Inc. 3193:Jean Marguin, pp. 64–65 (1994) 2599: 2586: 2583:, (2022). Retrieved 2022-09-02 2574: 2562: 2534: 2503: 2475: 1962:Académie des sciences de Paris 1392: 1380: 1356: 1353: 1341: 1332: 1302: 1299: 1293: 1284: 1254: 1242: 1212: 1206: 1183: 921: 918: 906: 897: 865: 853: 800: 797: 791: 782: 746: 740: 686: 680: 668: 644: 628:This can also be extended to: 598: 592: 540: 528: 499: 487: 426: 420: 13: 1: 3579: 3544: 3498: 3437:Williams, Michael R. (1997). 3436: 3349:. Kessinger Publishing, LLC. 3227: 3165: 3153: 3118: 2962:MORAR, FLORIN-STEFAN (2015). 2704: 2497: 2322:Schickard's calculating clock 1847: 3509: 3425: 3363: 3345:Ginsburg, Jekuthiel (2003). 3317: 3215: 2677: 2593: 2420:and initially used Pascal's 2118: 2115: 2110: 2093: 2090: 2085: 2071: 2068: 2062: 2042: 2039: 2030: 2014: 2011: 2003: 1982: 1979: 1973: 1953: 1950: 1944: 1929: 1926: 1918: 1903: 1900: 1894: 1516: 1464: 1415: 1134: 1086: 972: 961:marks on two adjacent spokes 379: 7: 3484:. Westport, CT: Greenwood. 3459: 3368:. Taipei: Caves Books, Ltd. 3276:(in French). Paris: Nathan. 2850:"Blaise Pascal (1623–1662)" 2515:"Blaise Pascal's Pascaline" 2427: 1470:inner wheels of complements 1362:{\displaystyle CP(CP(A-B))} 1070: 812:{\displaystyle CP(CP(A))=A} 765:inner wheels of complements 27:Early mechanical calculator 10: 3863: 3510:M.E.P (October 31, 1942). 3476:; Ferro, David L. (2005). 3464:Pascal, The life of genius 3426:d'Ocagne, Maurice (1893). 3236: 2848:Champan, S. (1942-10-01). 1923:Christina, Queen of Sweden 1227:during the first step and 838: 825: 725: 137: 3796: 3753: 3722: 3677: 3499:Perrault, Claude (1700). 3472: 3414: 3344: 3326: 3289: 3280: 3203: 3192: 3177: 3130: 3071: 3058:Oeuvres: Privilege Du Roi 2980:10.1017/S0007087414000429 2768: 2731: 2719: 2689: 2653: 2641: 2617: 2605: 2568: 2556: 2424:method for subtractions. 1610:. Length was measured in 1308:{\displaystyle CP(CP(A))} 1191:The accumulator contains 167:, which gave us both the 3364:Needham, Joseph (1986). 3265:Oeuvres de Blaise Pascal 2909:(in French). p. 12. 2469: 2160:King Louis XIV of France 1570:Pascalines came in both 3580:"Usage de la machine". 3460:Bishop, Morris (1936). 3394:Ifrah, Georges (2001). 3373:Ifrah, Georges (2000). 3281:Mourlevat, Guy (1988). 3263:Pascal, Blaise (1779). 3055:Pascal, Blaise (1779). 3030:Jones, Matthew (2016). 2920:Pascal, Blaise (1779). 2905:Mourlevat, Guy (1988). 2831:Pascal, Blaise (1645). 2368:University of Göttingen 1565: 1260:{\displaystyle CP(A-B)} 871:{\displaystyle CP(A-B)} 3837:Mechanical calculators 3415:Felt, Dorr E. (1916). 3294:(in French). Hermann. 3290:Marguin, Jean (1994). 2937:Heller, Henry (2002). 2351: 2340:University of Tübingen 2323: 2276: 2268: 2221: 2143: 2116: Accounting 1399: 1363: 1309: 1261: 1219: 940: 872: 813: 753: 711: 615: 458: 328: 297: 272: 263: 206: 198: 147: 43: 35: 3522:(3809). London: 527. 3168:, pp. 124, 128 (1997) 2926:(in French). La Haye. 2813:on November 21, 2005. 2513:(November 14, 2014). 2349: 2321: 2274: 2258: 2219: 2154:Intellectual property 2138: 1734:Decimal / scientific 1416:Change display space 1400: 1398:{\displaystyle (A-B)} 1364: 1310: 1262: 1220: 1218:{\displaystyle CP(A)} 955:Resetting the machine 941: 873: 814: 754: 752:{\displaystyle CP(A)} 712: 616: 459: 326: 295: 269: 261: 204: 193: 145: 59:mechanical calculator 41: 33: 3731:Lettres provinciales 3605:at Wikimedia Commons 3327:Taton, René (1969). 3318:Taton, René (1963). 3309:Taton, René (1949). 2398:abaque rhabdologique 2166:(a precursor to the 1377: 1323: 1317:which is A and then 1275: 1233: 1197: 888: 844: 773: 731: 635: 474: 411: 170:Lettres provinciales 101:chancellor of France 3694:Pascal's calculator 3563:1942Natur.150..508C 3557:. London: 508–509. 3528:1942Natur.150..527M 3204:Scripta Mathematica 2866:1942Natur.150..508C 2771:, Genealogy, (1988) 2707:, N°8, p. 9, (1986) 2630:Usage de la machine 2559:, p. 12 (1988) 1710: 831: 105:Louis XIV of France 49:(also known as the 47:Pascal's calculator 3336:Collectif (1942). 3133:, pp. 46-48 (1994) 2644:, pp. 31–33 (1988) 2352: 2324: 2277: 2269: 2267:, are on the right 2222: 2144: 1898:Chancelier Séguier 1708: 1395: 1359: 1305: 1257: 1215: 936: 868: 809: 749: 707: 611: 609: 454: 329: 302:Avis nécessaire... 298: 273: 264: 207: 199: 148: 51:arithmetic machine 44: 36: 3847:French inventions 3824: 3823: 3785:Marguerite Périer 3769:Jacqueline Pascal 3735:(1656–1657) 3709:Pascal's triangle 3635: 3601:Media related to 3356:978-0-7661-3835-3 3301:978-2-7056-6166-3 3255:978-2-9528068-4-8 3083:(fr) Wikisource: 2860:(3809): 508–509. 2581:Magazine Priciest 2520:Things that Count 2459:Analytical engine 2454:Difference engine 2355:Gottfried Leibniz 2332:Wilhelm Schickard 2314:Competing designs 2202:Gottfried Leibniz 2128: 2127: 2008:Marguerite Périer 1839: 1838: 1578:The contemporary 1563: 1562: 1559: 1558: 1512: 1511: 1460: 1459: 1181: 1180: 1177: 1176: 1130: 1129: 1068: 1067: 1064: 1063: 1016: 1015: 952: 951: 224:nine's complement 120:Gottfried Leibniz 16:(Redirected from 3854: 3814: 3813: 3804: 3803: 3789: 3781: 3773: 3765: 3746: 3736: 3704:Pascal's theorem 3664: 3657: 3650: 3641: 3640: 3634: 3600: 3585: 3576: 3574: 3572:10.1038/150508a0 3541: 3539: 3537:10.1038/150527a0 3506: 3495: 3483: 3469: 3467: 3456: 3444: 3433: 3422: 3411: 3390: 3369: 3360: 3341: 3332: 3323: 3314: 3305: 3286: 3277: 3268: 3259: 3231: 3225: 3219: 3213: 3207: 3201: 3195: 3190: 3181: 3175: 3169: 3166:Michael Williams 3163: 3157: 3154:Michael Williams 3151: 3145: 3140: 3134: 3128: 3122: 3116: 3110: 3103: 3097: 3094: 3088: 3081: 3075: 3069: 3063: 3062: 3052: 3046: 3045: 3027: 3016: 3015: 2959: 2953: 2952: 2934: 2928: 2927: 2917: 2911: 2910: 2902: 2896: 2895: 2877: 2875:10.1038/150508a0 2845: 2839: 2838: 2828: 2815: 2814: 2803: 2797: 2796: 2794: 2793: 2784:. Archived from 2778: 2772: 2766: 2760: 2759: 2757: 2756: 2747:. Archived from 2741: 2735: 2729: 2723: 2717: 2708: 2705:Courrier du CIBP 2702: 2693: 2687: 2681: 2675: 2669: 2663: 2657: 2651: 2645: 2639: 2633: 2627: 2621: 2615: 2609: 2603: 2597: 2590: 2584: 2578: 2572: 2566: 2560: 2554: 2545: 2538: 2532: 2531: 2529: 2527: 2507: 2501: 2495: 2489: 2482:Œuvres de Pascal 2479: 2439:Stepped reckoner 2410:Thomas de Colmar 2363:Stepped Reckoner 2148:tax commissioner 2122:6 x 10 + 20 + 12 2075:8 x 10 + 20 + 12 2046:3 x 10 + 20 + 12 2037: 2028:Clermont-Ferrand 2000:Clermont-Ferrand 1986:4 x 10 + 20 + 12 1957:6 x 10 + 20 + 12 1907:6 x 10 + 20 + 12 1855: 1854: 1711: 1707: 1523: 1522: 1476: 1475: 1424: 1423: 1413: 1406: 1404: 1402: 1401: 1396: 1370: 1368: 1366: 1365: 1360: 1316: 1314: 1312: 1311: 1306: 1268: 1266: 1264: 1263: 1258: 1226: 1224: 1222: 1221: 1216: 1141: 1140: 1094: 1093: 1084: 1028: 1027: 980: 979: 970: 947: 945: 943: 942: 937: 879: 877: 875: 874: 869: 830: 829: 820: 818: 816: 815: 810: 760: 758: 756: 755: 750: 723: 722: 716: 714: 713: 708: 620: 618: 617: 612: 610: 579: 557: 556: 518: 517: 463: 461: 460: 455: 441: 440: 374: 373:pawl/ratchet (C) 370: 366: 362: 361:pawl/ratchet (C) 358: 350: 343: 342:pawl/ratchet (C) 339: 128:Thomas de Colmar 21: 3862: 3861: 3857: 3856: 3855: 3853: 3852: 3851: 3827: 3826: 3825: 3820: 3792: 3787: 3779: 3777:Gilberte Périer 3771: 3763: 3749: 3744: 3734: 3718: 3687: 3673: 3668: 3593: 3588: 3492: 3474:Swedin, Eric G. 3453: 3408: 3387: 3357: 3302: 3256: 3239: 3234: 3230:, p. 38 (1700). 3228:Claude Perrault 3226: 3222: 3214: 3210: 3206:, p. 149 (1932) 3202: 3198: 3191: 3184: 3176: 3172: 3164: 3160: 3156:, p. 122 (1997) 3152: 3148: 3141: 3137: 3129: 3125: 3121:, p. 20, (1984) 3117: 3113: 3104: 3100: 3095: 3091: 3082: 3078: 3070: 3066: 3053: 3049: 3042: 3028: 3019: 2960: 2956: 2949: 2935: 2931: 2918: 2914: 2903: 2899: 2846: 2842: 2829: 2818: 2805: 2804: 2800: 2791: 2789: 2780: 2779: 2775: 2767: 2763: 2754: 2752: 2743: 2742: 2738: 2730: 2726: 2718: 2711: 2703: 2696: 2688: 2684: 2676: 2672: 2664: 2660: 2652: 2648: 2640: 2636: 2628: 2624: 2616: 2612: 2604: 2600: 2594:Magazine Nature 2591: 2587: 2579: 2575: 2571:, p. 316 (1933) 2567: 2563: 2555: 2548: 2539: 2535: 2525: 2523: 2508: 2504: 2498:Magazine Nature 2496: 2492: 2480: 2476: 2472: 2430: 2328:Johannes Kepler 2316: 2297:royal privilege 2253: 2185: 2164:royal privilege 2156: 2133: 2066:Queen of Poland 2035: 2027: 1998: 1970: 1941: 1915: 1891: 1883: 1879: 1875: 1871: 1867: 1863: 1859: 1850: 1832: 1825: 1818: 1811: 1806: 1794: 1787: 1780: 1775: 1770: 1758: 1753: 1748: 1743: 1738: 1709:Configurations 1580:French currency 1568: 1378: 1375: 1374: 1372: 1324: 1321: 1320: 1318: 1276: 1273: 1272: 1270: 1234: 1231: 1230: 1228: 1198: 1195: 1194: 1192: 1186: 1073: 957: 889: 886: 885: 883: 845: 842: 841: 839: 827: 826: 774: 771: 770: 768: 732: 729: 728: 726: 636: 633: 632: 608: 607: 577: 576: 552: 548: 543: 513: 509: 502: 477: 475: 472: 471: 436: 432: 412: 409: 408: 391: 382: 372: 369:buffer stop (R) 368: 364: 360: 356: 348: 341: 337: 290: 288:Carry mechanism 256: 254:Inner mechanism 236:machine tardive 153:Royal Privilege 140: 109:royal privilege 74:carry mechanism 28: 23: 22: 15: 12: 11: 5: 3860: 3850: 3849: 3844: 3839: 3822: 3821: 3819: 3818: 3808: 3797: 3794: 3793: 3791: 3790: 3782: 3774: 3766: 3761:Étienne Pascal 3757: 3755: 3751: 3750: 3748: 3747: 3737: 3726: 3724: 3720: 3719: 3717: 3716: 3714:Pascal's wager 3711: 3706: 3701: 3696: 3690: 3688: 3686: 3685: 3682: 3678: 3675: 3674: 3667: 3666: 3659: 3652: 3644: 3638: 3637: 3626: 3621: 3616: 3611: 3606: 3592: 3591:External links 3589: 3587: 3586: 3577: 3542: 3507: 3496: 3490: 3470: 3457: 3451: 3434: 3423: 3412: 3406: 3391: 3385: 3370: 3361: 3355: 3342: 3333: 3324: 3315: 3306: 3300: 3287: 3278: 3269: 3260: 3254: 3240: 3238: 3235: 3233: 3232: 3220: 3208: 3196: 3182: 3180:, p. 11 (2005) 3170: 3158: 3146: 3135: 3123: 3111: 3098: 3089: 3076: 3074:, p. 46 (1994) 3064: 3047: 3040: 3017: 2974:(1): 123–146. 2954: 2947: 2929: 2912: 2897: 2840: 2816: 2798: 2773: 2761: 2736: 2734:, p. 38 (1988) 2724: 2722:, p. 30 (1988) 2709: 2694: 2692:, p. 17 (1988) 2682: 2680:, p. 41 (1994) 2670: 2658: 2656:, p. 27 (1988) 2646: 2634: 2622: 2610: 2598: 2585: 2573: 2561: 2546: 2533: 2502: 2490: 2484:in 5 volumes, 2473: 2471: 2468: 2467: 2466: 2461: 2456: 2451: 2446: 2441: 2436: 2434:Adding machine 2429: 2426: 2422:9's complement 2418:Leibniz wheels 2387:Samuel Morland 2383:Tito Burattini 2315: 2312: 2311: 2310: 2307: 2300: 2293: 2290: 2287: 2284: 2252: 2249: 2234:Peter Blondeau 2230:Samuel Morland 2184: 2181: 2176:King Louis XIV 2172:Pierre Séguier 2162:gave Pascal a 2155: 2152: 2132: 2129: 2126: 2125: 2123: 2120: 2117: 2114: 2112: 2109: 2102: 2101: 2098: 2095: 2092: 2089: 2087: 2084: 2080: 2079: 2076: 2073: 2070: 2067: 2064: 2061: 2051: 2050: 2047: 2044: 2041: 2038: 2032: 2029: 2023: 2022: 2019: 2016: 2013: 2010: 2005: 2002: 1991: 1990: 1987: 1984: 1981: 1978: 1977:Late (Tardive) 1975: 1972: 1966: 1965: 1958: 1955: 1952: 1949: 1946: 1943: 1937: 1936: 1934: 1931: 1928: 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419: 416: 390: 389:9's complement 387: 381: 378: 377: 376: 353: 345: 289: 286: 255: 252: 139: 136: 124:Leibniz wheels 111:(similar to a 107:gave Pascal a 97:Pierre Séguier 26: 9: 6: 4: 3: 2: 3859: 3848: 3845: 3843: 3842:Blaise Pascal 3840: 3838: 3835: 3834: 3832: 3817: 3809: 3807: 3799: 3798: 3795: 3786: 3783: 3778: 3775: 3770: 3767: 3762: 3759: 3758: 3756: 3752: 3743: 3742: 3738: 3733: 3732: 3728: 3727: 3725: 3721: 3715: 3712: 3710: 3707: 3705: 3702: 3700: 3697: 3695: 3692: 3691: 3689: 3683: 3680: 3679: 3676: 3672: 3671:Blaise Pascal 3665: 3660: 3658: 3653: 3651: 3646: 3645: 3642: 3633: 3632: 3627: 3625: 3622: 3620: 3617: 3615: 3612: 3610: 3607: 3604: 3599: 3595: 3594: 3583: 3578: 3573: 3568: 3564: 3560: 3556: 3552: 3548: 3543: 3538: 3533: 3529: 3525: 3521: 3517: 3513: 3508: 3504: 3503: 3497: 3493: 3491:0-8018-8774-7 3487: 3482: 3481: 3475: 3471: 3466: 3465: 3458: 3454: 3452:0-8186-7739-2 3448: 3443: 3442: 3435: 3431: 3430: 3424: 3420: 3419: 3413: 3409: 3407:0-471-39671-0 3403: 3399: 3398: 3392: 3388: 3386:0-471-39671-0 3382: 3378: 3377: 3371: 3367: 3362: 3358: 3352: 3348: 3343: 3339: 3334: 3330: 3325: 3321: 3316: 3312: 3307: 3303: 3297: 3293: 3288: 3284: 3279: 3275: 3270: 3266: 3261: 3257: 3251: 3247: 3242: 3241: 3229: 3224: 3217: 3212: 3205: 3200: 3194: 3189: 3187: 3179: 3174: 3167: 3162: 3155: 3150: 3144: 3139: 3132: 3127: 3120: 3119:Stan Augarten 3115: 3108: 3102: 3093: 3086: 3080: 3073: 3068: 3060: 3059: 3051: 3043: 3041:9780226411460 3037: 3033: 3026: 3024: 3022: 3013: 3009: 3005: 3001: 2997: 2993: 2989: 2985: 2981: 2977: 2973: 2969: 2965: 2958: 2950: 2944: 2940: 2933: 2925: 2924: 2916: 2908: 2901: 2893: 2889: 2885: 2881: 2876: 2871: 2867: 2863: 2859: 2855: 2851: 2844: 2836: 2835: 2827: 2825: 2823: 2821: 2812: 2808: 2802: 2788:on 2011-10-19 2787: 2783: 2777: 2770: 2769:Guy Mourlevat 2765: 2751:on 2011-10-15 2750: 2746: 2740: 2733: 2732:Guy Mourlevat 2728: 2721: 2720:Guy Mourlevat 2716: 2714: 2706: 2701: 2699: 2691: 2690:Guy Mourlevat 2686: 2679: 2674: 2667: 2662: 2655: 2654:Guy Mourlevat 2650: 2643: 2642:Guy Mourlevat 2638: 2631: 2626: 2619: 2618:Guy Mourlevat 2614: 2607: 2606:Guy Mourlevat 2602: 2595: 2589: 2582: 2577: 2570: 2565: 2558: 2557:Guy Mourlevat 2553: 2551: 2543: 2537: 2522: 2521: 2516: 2512: 2506: 2499: 2494: 2487: 2483: 2478: 2474: 2465: 2464:Z1 (computer) 2462: 2460: 2457: 2455: 2452: 2450: 2447: 2445: 2442: 2440: 2437: 2435: 2432: 2431: 2425: 2423: 2419: 2415: 2411: 2406: 2402: 2399: 2394: 2392: 2388: 2384: 2379: 2377: 2376:Leibniz wheel 2371: 2369: 2364: 2359: 2356: 2348: 2344: 2341: 2336: 2333: 2329: 2320: 2308: 2305: 2304:encyclopaedia 2301: 2298: 2294: 2291: 2288: 2285: 2282: 2281: 2280: 2273: 2266: 2262: 2257: 2248: 2245: 2243: 2239: 2235: 2231: 2228:In contrast, 2226: 2218: 2214: 2211: 2205: 2203: 2198: 2194: 2190: 2189:Ancien Régime 2180: 2177: 2173: 2169: 2165: 2161: 2151: 2149: 2142: 2137: 2124: 2121: 2113: 2107: 2104: 2103: 2099: 2096: 2088: 2082: 2081: 2077: 2074: 2065: 2060: 2056: 2053: 2052: 2048: 2045: 2036:Durant-Pascal 2033: 2025: 2024: 2020: 2017: 2009: 2006: 2001: 1997: 1993: 1992: 1988: 1985: 1976: 1968: 1967: 1963: 1959: 1956: 1947: 1939: 1938: 1935: 1932: 1924: 1921: 1913: 1912: 1909: 1906: 1897: 1890: 1887: 1886: 1881: 1878:Configuration 1877: 1873: 1869: 1865: 1861: 1857: 1856: 1853: 1845: 1842: 1835: 1830: 1828: 1823: 1821: 1816: 1814: 1809: 1804: 1801: 1800: 1797: 1792: 1790: 1785: 1783: 1778: 1773: 1768: 1765: 1764: 1761: 1756: 1751: 1746: 1741: 1736: 1733: 1732: 1728: 1725: 1722: 1719: 1717:Other wheels 1716: 1714:Machine type 1713: 1712: 1706: 1704: 1700: 1696: 1692: 1688: 1684: 1680: 1676: 1672: 1668: 1664: 1660: 1655: 1653: 1649: 1645: 1641: 1637: 1633: 1629: 1628: 1624: 1620: 1615: 1614: 1609: 1605: 1601: 1597: 1593: 1589: 1585: 1581: 1576: 1573: 1554: 1552: 2 1551: 1549: 0 1548: 1546: 8 1545: 1543: 5 1542: 1541: 1537: 1535: 7 1534: 1532: 9 1531: 1529: 1 1528: 1526: 4 1525: 1524: 1521: 1518: 1515: 1507: 1505: 7 1504: 1502: 6 1501: 1499: 5 1498: 1496: 4 1495: 1494: 1490: 1488: 2 1487: 1485: 3 1484: 1482: 4 1481: 1479: 5 1478: 1477: 1474: 1471: 1467: 1463: 1455: 1453: 0 1452: 1450: 0 1449: 1447: 0 1446: 1444: 0 1443: 1442: 1438: 1436: 9 1435: 1433: 9 1432: 1430: 9 1429: 1427: 9 1426: 1425: 1422: 1418: 1414: 1411: 1408: 1389: 1386: 1383: 1350: 1347: 1344: 1338: 1335: 1329: 1326: 1296: 1290: 1287: 1281: 1278: 1251: 1248: 1245: 1239: 1236: 1209: 1203: 1200: 1189: 1172: 1170: 3 1169: 1167: 1 1166: 1164: 9 1163: 1161: 6 1160: 1159: 1155: 1153: 6 1152: 1150: 8 1149: 1147: 0 1146: 1144: 3 1143: 1142: 1139: 1136: 1133: 1125: 1123: 4 1122: 1120: 3 1119: 1117: 2 1116: 1114: 1 1113: 1112: 1108: 1106: 5 1105: 1103: 6 1102: 1100: 7 1099: 1097: 8 1096: 1095: 1092: 1089: 1085: 1082: 1079: 1076: 1059: 1057: 0 1056: 1054: 0 1053: 1051: 0 1050: 1048: 0 1047: 1046: 1042: 1040: 9 1039: 1037: 9 1036: 1034: 9 1033: 1031: 9 1030: 1029: 1026: 1023: 1020: 1019: 1011: 1009: 9 1008: 1006: 9 1005: 1003: 9 1002: 1000: 9 999: 998: 994: 992: 0 991: 989: 0 988: 986: 0 985: 983: 0 982: 981: 978: 975: 971: 968: 964: 962: 933: 930: 927: 924: 915: 912: 909: 903: 900: 894: 891: 881: 862: 859: 856: 850: 847: 837: 833: 824: 806: 803: 794: 788: 785: 779: 776: 766: 762: 743: 737: 734: 724: 721: 704: 701: 698: 695: 692: 689: 683: 677: 674: 671: 665: 662: 659: 656: 653: 650: 647: 641: 638: 631: 630: 629: 626: 604: 601: 595: 589: 586: 583: 581: 573: 570: 567: 564: 561: 558: 553: 549: 545: 537: 534: 531: 525: 522: 519: 514: 510: 506: 504: 496: 493: 490: 484: 481: 470: 469: 468: 451: 448: 445: 442: 437: 433: 429: 423: 417: 414: 407: 406: 405: 402: 400: 396: 386: 371:. The upper 354: 352:disconnected. 346: 334: 333: 332: 325: 321: 319: 318:Domino effect 313: 309: 307: 303: 294: 285: 281: 279: 268: 260: 251: 247: 243: 239: 237: 232: 228: 225: 220: 216: 213: 203: 197: 192: 188: 185: 180: 178: 177: 172: 171: 166: 162: 156: 154: 144: 135: 133: 130:designed his 129: 125: 122:invented his 121: 116: 114: 110: 106: 102: 98: 94: 89: 87: 83: 82:turret clocks 79: 75: 70: 68: 64: 63:Blaise Pascal 60: 56: 52: 48: 40: 32: 19: 3739: 3729: 3699:Pascal's law 3693: 3629: 3581: 3554: 3550: 3519: 3515: 3501: 3479: 3463: 3440: 3428: 3417: 3396: 3375: 3365: 3346: 3337: 3328: 3319: 3310: 3291: 3282: 3273: 3264: 3245: 3223: 3216:Jean Marguin 3211: 3199: 3173: 3161: 3149: 3138: 3131:Jean Marguin 3126: 3114: 3105:Wikisource: 3101: 3092: 3079: 3072:Jean Marguin 3067: 3057: 3050: 3031: 2971: 2967: 2957: 2938: 2932: 2922: 2915: 2906: 2900: 2857: 2853: 2843: 2833: 2811:the original 2801: 2790:. Retrieved 2786:the original 2776: 2764: 2753:. Retrieved 2749:the original 2739: 2727: 2685: 2678:Jean Marguin 2673: 2661: 2649: 2637: 2629: 2625: 2613: 2601: 2588: 2576: 2569:Leland Locke 2564: 2544:, Wikisource 2536: 2524:. Retrieved 2519: 2505: 2493: 2485: 2481: 2477: 2444:Arithmometer 2414:arithmometer 2407: 2403: 2397: 2395: 2391:René Grillet 2380: 2372: 2360: 2353: 2337: 2325: 2296: 2278: 2264: 2260: 2251:Achievements 2246: 2227: 2223: 2206: 2186: 2157: 2145: 2140: 1961: 1948:Louis Périer 1851: 1843: 1840: 1833: 1826: 1819: 1812: 1795: 1788: 1781: 1759: 1702: 1698: 1694: 1690: 1686: 1682: 1678: 1674: 1670: 1666: 1662: 1658: 1656: 1651: 1647: 1643: 1639: 1635: 1631: 1626: 1622: 1618: 1611: 1607: 1603: 1599: 1595: 1591: 1587: 1583: 1582:system used 1577: 1569: 1465:Subtraction 1409: 1190: 1187: 1080: 1077: 1074: 965: 958: 719: 627: 623: 466: 403: 398: 394: 392: 383: 355:The kicking 349:spring (z,u) 330: 314: 310: 305: 299: 282: 278:lantern gear 274: 248: 244: 240: 235: 233: 229: 221: 217: 208: 195: 184:World War II 181: 174: 168: 157: 149: 132:arithmometer 117: 90: 86:water wheels 78:lantern gear 71: 61:invented by 54: 50: 46: 45: 3681:Innovations 3178:Eric Swedin 2526:January 31, 2449:Comptometer 2210:hylomorphic 2197:Clockmakers 1996:Henri Lecoq 1994:Musée 1969:CNAM museum 1940:CNAM museum 1914:CNAM museum 1889:CNAM museum 1766:Accounting 1184:Subtraction 296:The sautoir 212:rotary dial 205:Input wheel 3831:Categories 2948:0521893801 2792:2011-11-05 2755:2011-11-19 2242:Fromanteel 2108:collection 2069:Accounting 2040:Accounting 2034:Chevalier 2012:Scientific 1980:Accounting 1951:Accounting 1927:Scientific 1901:Accounting 1848:Production 1802:Surveying 1744:Thousands 625:machines. 165:philosophy 93:prototypes 80:, used in 3603:Pascaline 2988:0007-0874 2884:1476-4687 2511:Falk, Jim 2238:Richelieu 2158:In 1649, 2091:Surveying 1964:in 1711. 1771:Hundreds 1749:Hundreds 1387:− 1371:which is 1348:− 1249:− 1087:Addition 931:− 913:− 860:− 663:− 657:− 651:− 565:− 559:− 535:− 526:− 520:− 494:− 449:− 443:− 380:Operation 367:hits the 55:Pascaline 18:Pascalina 3806:Category 3780:(sister) 3772:(sister) 3764:(father) 3012:38193192 3004:25833800 2996:43820570 2596:, (1942) 2500:, (1942) 2428:See also 2299:of 1649) 1858:Location 1594:with 20 1071:Addition 973:Re-zero 365:part (T) 357:pawl (1) 338:pawl (1) 173:and the 161:religion 3816:Commons 3788:(niece) 3741:Pensées 3559:Bibcode 3524:Bibcode 3237:Sources 3218:, p. 66 2892:4097256 2862:Bibcode 2486:La Haye 2265:deniers 2063:Germany 2059:Dresden 1862:Country 1831:base 12 1824:base 12 1810:base 10 1805:base 10 1796:Deniers 1793:base 12 1786:base 20 1779:base 10 1774:base 10 1769:base 10 1757:base 10 1752:base 10 1747:base 10 1742:base 10 1737:base 10 1675:deniers 1671:deniers 1646:and 12 1630:with 6 1604:deniers 1602:and 12 1592:deniers 1572:decimal 1405:⁠ 1373:⁠ 1369:⁠ 1319:⁠ 1315:⁠ 1271:⁠ 1267:⁠ 1229:⁠ 1225:⁠ 1193:⁠ 1021: 946:⁠ 884:⁠ 878:⁠ 840:⁠ 819:⁠ 769:⁠ 759:⁠ 727:⁠ 196:sautoir 176:Pensées 138:History 99:, then 57:) is a 3754:Family 3745:(1669) 3684:Career 3631:BibNum 3551:Nature 3516:Nature 3488: 3449: 3404: 3383: 3353: 3298: 3252: 3038: 3010: 3002: 2994: 2986: 2945: 2890: 2882: 2854:Nature 2488:, 1779 2193:guilds 2168:patent 2086:France 2031:France 2018:8 x 10 2004:France 1974:France 1945:France 1933:6 x 10 1919:France 1895:France 1874:Wheels 1834:Lignes 1827:Pouces 1817:base 6 1813:Toises 1782:Livres 1703:lignes 1701:) and 1699:lignes 1695:pouces 1691:pouces 1679:toises 1673:) and 1659:livres 1648:lignes 1640:pouces 1627:lignes 1623:pouces 1613:toises 1584:livres 306:sauter 113:patent 3723:Works 3008:S2CID 2992:JSTOR 2888:S2CID 2540:(fr) 2470:Notes 1971:Paris 1942:Paris 1916:Paris 1892:Paris 1882:Notes 1820:Pieds 1807:Tens 1776:Tens 1760:Units 1754:Tens 1687:pieds 1683:pieds 1652:pouce 1650:to a 1642:to a 1638:, 12 1636:toise 1634:to a 1632:pieds 1619:pieds 1606:to a 1600:livre 1598:to a 397:is 9- 67:Rouen 3486:ISBN 3447:ISBN 3402:ISBN 3381:ISBN 3351:ISBN 3296:ISBN 3250:ISBN 3036:ISBN 3000:PMID 2984:ISSN 2943:ISBN 2880:ISSN 2528:2016 2389:and 2263:and 2261:sols 1870:Type 1789:Sols 1729:1st 1726:2nd 1723:3rd 1720:4th 1697:(12 1689:(12 1669:(12 1667:sols 1663:sols 1661:(20 1644:pied 1625:and 1596:sols 1590:and 1588:sols 1566:Uses 163:and 84:and 3567:doi 3555:150 3532:doi 3520:150 2976:doi 2870:doi 2858:150 2393:). 2111:USA 2106:IBM 1693:), 1685:), 1681:(6 1665:), 1608:sol 53:or 3833:: 3565:. 3553:. 3549:. 3530:. 3518:. 3514:. 3185:^ 3020:^ 3006:. 2998:. 2990:. 2982:. 2972:48 2970:. 2966:. 2886:. 2878:. 2868:. 2856:. 2852:. 2819:^ 2712:^ 2697:^ 2549:^ 2517:. 2385:, 2370:. 2072:10 2057:, 1621:, 1616:, 1586:, 821:. 550:10 511:10 434:10 179:. 3663:e 3656:t 3649:v 3636:. 3575:. 3569:: 3561:: 3540:. 3534:: 3526:: 3494:. 3455:. 3410:. 3389:. 3359:. 3304:. 3258:. 3044:. 3014:. 2978:: 2951:. 2894:. 2872:: 2864:: 2837:. 2795:. 2758:. 2530:. 2119:8 2094:8 2043:5 2015:8 1983:6 1954:8 1930:6 1904:8 1393:) 1390:B 1384:A 1381:( 1357:) 1354:) 1351:B 1345:A 1342:( 1339:P 1336:C 1333:( 1330:P 1327:C 1303:) 1300:) 1297:A 1294:( 1291:P 1288:C 1285:( 1282:P 1279:C 1255:) 1252:B 1246:A 1243:( 1240:P 1237:C 1213:) 1210:A 1207:( 1204:P 1201:C 934:B 928:A 925:= 922:) 919:) 916:B 910:A 907:( 904:P 901:C 898:( 895:P 892:C 866:) 863:B 857:A 854:( 851:P 848:C 828:B 807:A 804:= 801:) 798:) 795:A 792:( 789:P 786:C 783:( 780:P 777:C 747:) 744:A 741:( 738:P 735:C 705:D 702:+ 699:C 696:+ 693:B 690:+ 687:) 684:A 681:( 678:P 675:C 672:= 669:) 666:D 660:C 654:B 648:A 645:( 642:P 639:C 605:B 602:+ 599:) 596:A 593:( 590:P 587:C 584:= 574:B 571:+ 568:A 562:1 554:n 546:= 541:) 538:B 532:A 529:( 523:1 515:n 507:= 500:) 497:B 491:A 488:( 485:P 482:C 452:A 446:1 438:n 430:= 427:) 424:A 421:( 418:P 415:C 399:d 395:d 20:)

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Pascal's calculator

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